Effects of sediment on the photosynthesis of adult corals
Lillian J. Tuttle
9/25/2020
These datasets contain information from multiple articles (Ref_name) and studies/experiments (Ref) within those articles about the effects of DEPOSITED & SUSPENDED sediment on the photosynthetic yield (Fv/Fm or deltaF/Fm) or the photosynthesis-respiration (P/R) ratio of symbiotic algae living within coral cells. I would like to explore the dose-response relationship between sediment ‘dose’ and the effect size, estimated here as the standardized mean difference between treatment and control, in terms of Hedges’ d:
Hedges’ d is the standardized mean difference between the treatment and control groups (Hedges and Olkin 1985). Each study may have multiple Hedges’ d calculations, one for each treatment-control comparison at each time-point.
‘Dose’ can be quantified as sediment exposure concentration (mg/cm2/day for deposited sediment and mg/L for suspended sediment), exposure duration (days), or as “cumulative exposure”, for which I multiply concentration and duration (mg/cm2 for deposited sediment and mg x day/L for suspended sediment).
Each study/experiment (Ref) may contain multiple sets of controls and treatments (due to using multiple species or sediment types, for instance). Thus, I have added two categorical vectors, ‘Comparison’ and ‘Control’, which group each set of control-treatment comparisons into a unique two-letter code, within which is one control (Control==“1”) and at least one treatment (Control==“0”). Therefore, ‘Comparison’ is nested within ‘Ref’, which is further nested within ‘Ref_name’.
I. Photosynthetic Efficiency
A. Deposited Sediment
1. Plots
I calculated the standardized mean difference in terms of Hedges’ d and plot it here with respect to cumulative exposure. I did this first for a Hedges’ d that I calculated before importing the data to R and again for a Hedges’ d that is calculated by the dosresmeta::covar.smd function.
It is interesting that there is a difference between how I calculated Hedges’ d and how dosresmeta appears to calculate it. But in both cases, there may be a negative relationship between sediment exposure and effect size. There does not appear to be strong effects of phylogeny (genus) or geography (ocean and region). There may be effects of sediment type (source, origin, grain size), but I do not think these will be discernible given the variance.
2. Model Fitting
The following set of functions model fixed and random (nested) effects WITHOUT accounting for within-comparison (or within-study) correlations. The output for each is a univariate, random-effects meta-regression.
To account for within-comparison correlations in the mixmeta model, I replace the ‘S’ argument with a ‘control’ argument, which requires me to provide the covariance matrices, as done with the covar.smd function.
And now to compare relative fit of linear models…
## df AIC
## mod_DS_photo_1d 2 922.2444
## mod_DS_photo_2d 3 890.3866
## mod_DS_photo_3d 3 921.5338
## mod_DS_photo_4d 4 892.4020
## mod_DS_photo_5d 2 802.3665
## mod_DS_photo_6d 3 784.3571
## mod_DS_photo_7d 3 786.4533## df AIC
## alt_mod_DS_photo_6d 8 626.9708
## mod_DS_photo_6d 3 784.3571And now to evaluate residuals of models…
Patterns: 1. “Clumping” of residuals that may be improved by log-transformation. 2. The angle of the residual line does not look good for alternative models. 3. First let’s try a log transformation of sediment exposure for both alt and normal models.
Now let’s check out a log, base 10 transformation of sediment exposure to see if it improves the residuals of the models.
To account for within-comparison correlations in the mixmeta model, I replace the ‘S’ argument with a ‘control’ argument, which requires me to provide the covariance matrices, as done with the covar.smd function.
3. Model Comparison and Summary
And now to compare relative fit of log-linear models…
## df AIC
## log_mod_DS_photo_1d 2 872.3795
## log_mod_DS_photo_2d 3 850.9231
## log_mod_DS_photo_3d 3 870.7125
## log_mod_DS_photo_4d 4 852.9231
## log_mod_DS_photo_5d 2 788.6034
## log_mod_DS_photo_6d 3 771.2589
## log_mod_DS_photo_7d 3 773.9565## df AIC
## alt_log_mod_DS_photo_6d 8 629.9006
## log_mod_DS_photo_6d 3 771.2589And now to evaluate residuals of models…
Patterns: 1. Log model much improves residuals – lower magnitudes and more even spread. 2. Alt model looks terrible – high magnitude residuals and severe misalignment between residual points and model average (zero abline).
4. Best-Fit Model Summary
MG/CM2/DAY IS PREDICTOR, Model using dosresmeta calculation of Hedges’ d
Now I will predict the effect size along the exposure range and plot with confidence intervals.
## Call: mixmeta(formula = smd ~ 0 + log10_mg_cm2_d, data = ES_DS_fv_fm2,
## random = ~0 + log10_mg_cm2_d | Ref/Comparison, method = "ml",
## control = list(addSlist = newlist_log_FVFM2))
##
## Univariate extended random-effects meta-regression
## Dimension: 1
## Estimation method: ML
##
## Fixed-effects coefficients
## Estimate Std. Error z Pr(>|z|) 95%ci.lb 95%ci.ub
## log10_mg_cm2_d -0.5942 0.2138 -2.7794 0.0054 -1.0132 -0.1752 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Random-effects (co)variance components
## Formula: ~0 + log10_mg_cm2_d | Ref
## Structure: General positive-definite
## Std. Dev
## 0.5548
##
## Formula: ~0 + log10_mg_cm2_d | Comparison
## Structure: General positive-definite
## Std. Dev
## 0.0000
##
## Univariate Cochran Q-test for residual heterogeneity:
## Q = 604.2709 (df = 140), p-value = 0.0000
## I-square statistic = 76.8%
##
## 141 units, 1 outcome, 141 observations, 1 fixed and 2 random-effects parameters
## logLik AIC BIC
## -382.6294 771.2589 780.1052
B. Suspended Sediment
1. Plots
I calculated the standardized mean difference in terms of Hedges’ d and plot it here with respect to exposure concentration. I did this first for a Hedges’ d that I calculated before importing the data to R and again for a Hedges’ d that is calculated by the dosresmeta::covar.smd function.
It is interesting that there is a difference between how I calculated Hedges’ d and how dosresmeta appears to calculate it. But in both cases, there is a funnel-like relationship between sediment exposure and effect size. There does not appear to be strong effects of phylogeny (genus) or geography (ocean and region). There may be effects of sediment type (source, origin, grain size), but these will likely be indiscernible, given the variance.
2. Model Fitting
The following set of functions model fixed and random (nested) effects WITHOUT accounting for within-comparison (or within-study) correlations. The output for each is a univariate, random-effects meta-regression.
To account for within-comparison correlations in the mixmeta model, I replace the ‘S’ argument with a ‘control’ argument, which requires me to provide the covariance matrices, as done with the covar.smd function.
And now to compare relative fit of linear models…
## df AIC
## mod_SS_photo_1d 5 299.9027
## mod_SS_photo_2d 8 305.9064
## mod_SS_photo_3d 8 305.9062
## mod_SS_photo_4d 11 311.9036
## mod_SS_photo_5d 5 285.0028
## mod_SS_photo_6d 8 290.6513
## mod_SS_photo_7d 8 290.8876And now to evaluate residuals of models…
Patterns: 1. Not bad – not high magnitude of residuals and does not look like it requires transformations or non-linear approaches.
4. Best-Fit Model Summary
MG/L IS PREDICTOR, Model using dosresmeta calculation of Hedges’ d
Now I will predict the effect size along the exposure range and plot with confidence intervals.
## Call: mixmeta(formula = smd ~ Sed_level_standardized, data = ES_SS_fv_fm2,
## random = ~Sed_level_standardized | Comparison, method = "ml",
## control = list(addSlist = newlist_FVFM_SS))
##
## Univariate extended random-effects meta-regression
## Dimension: 1
## Estimation method: ML
##
## Fixed-effects coefficients
## Estimate Std. Error z Pr(>|z|) 95%ci.lb
## (Intercept) -0.2325 0.0796 -2.9202 0.0035 -0.3886
## Sed_level_standardized 0.0034 0.0012 2.8053 0.0050 0.0010
## 95%ci.ub
## (Intercept) -0.0765 **
## Sed_level_standardized 0.0058 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Random-effects (co)variance components
## Formula: ~Sed_level_standardized | Comparison
## Structure: General positive-definite
## Std. Dev Corr
## (Intercept) 0.0002 (Intercept)
## Sed_level_standardized 0.0045 0.1527
##
## Univariate Cochran Q-test for residual heterogeneity:
## Q = 206.1245 (df = 162), p-value = 0.0109
## I-square statistic = 21.4%
##
## 164 units, 1 outcome, 164 observations, 2 fixed and 3 random-effects parameters
## logLik AIC BIC
## -137.5014 285.0028 300.5021
II. Photosynthesis-Respiration Ratio
A. Deposited Sediment
1. Plots
I calculated the standardized mean difference in terms of Hedges’ d and plot it here with respect to exposure concentration. I did this first for a Hedges’ d that I calculated before importing the data to R and again for a Hedges’ d that is calculated by the dosresmeta::covar.smd function.
It is interesting that there is a difference between how I calculated Hedges’ d and how dosresmeta appears to calculate it. But in both cases, there may be a negative relationship between sediment exposure and effect size. There does not appear to be strong effects of phylogeny (genus) or geography (ocean and region). There may be effects of sediment type (source, origin, grain size), but I do not think these will be discernible given the variance.
2. Model Fitting
The following set of functions model fixed and random (nested) effects WITHOUT accounting for within-comparison (or within-study) correlations. The output for each is a univariate, random-effects meta-regression.
To account for within-comparison correlations in the mixmeta model, I replace the ‘S’ argument with a ‘control’ argument, which requires me to provide the covariance matrices, as done with the covar.smd function.
3. Model Comparison and Summary
And now to compare relative fit of linear models…
## df AIC
## mod_DS_p_r_1d 5 47.00097
## mod_DS_p_r_5d 5 47.00097And now to evaluate residuals of models…
Patterns: 1. Sparse data, but they all seem to fit a linear trend with minimal residual magnitudes.
4. Best-Fit Model Summary
MG/CM2/DAY IS PREDICTOR, Model using dosresmeta calculation of Hedges’ d
Now I will predict the effect size along the exposure range and plot with confidence intervals.
## Call: mixmeta(formula = smd ~ Sed_level_standardized, data = ES_DS_p_r2,
## random = ~Sed_level_standardized | Comparison, method = "ml",
## control = list(addSlist = newlist_PR))
##
## Univariate extended random-effects meta-regression
## Dimension: 1
## Estimation method: ML
##
## Fixed-effects coefficients
## Estimate Std. Error z Pr(>|z|) 95%ci.lb
## (Intercept) -2.9895 1.1724 -2.5499 0.0108 -5.2874
## Sed_level_standardized 0.0393 0.0229 1.7114 0.0870 -0.0057
## 95%ci.ub
## (Intercept) -0.6917 *
## Sed_level_standardized 0.0843 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Random-effects (co)variance components
## Formula: ~Sed_level_standardized | Comparison
## Structure: General positive-definite
## Std. Dev Corr
## (Intercept) 2.3227 (Intercept)
## Sed_level_standardized 0.0384 -1
##
## Univariate Cochran Q-test for residual heterogeneity:
## Q = 19.2302 (df = 8), p-value = 0.0137
## I-square statistic = 58.4%
##
## 10 units, 1 outcome, 10 observations, 2 fixed and 3 random-effects parameters
## logLik AIC BIC
## -18.5005 47.0010 48.5139